We define a class of Lyndon words, called Christoffel-Lyndon words. We
show that they are in bijection with n-tuples of relatively prime
natural numbers. We give a geometrical interpretation of these words.
They are linked to an algorithm of Euclidean type. It admits an
extension to n-tuples of real numbers; we show that if the algorithm is
periodic, then these real numbers are algebraic of degree at most n and
that the associated multidimensional continued fraction converges to
these numbers.